How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?
8 . ^{6}C_{4} . ^{7}C_{4}
6 . 7 . ^{8}C_{4}_{}
6 . 8 . ^{7}C_{4}
7 . ^{6}C4 . ^{8}C4
D.
7 . ^{6}C4 . ^{8}C4
Other than S, seven letters M, I, I, I, P, P, I can be arranged in 7!/2! 4!=7 . 5 . 3.
Now four S can be placed in 8 spaces in 8 C4 ways. Desired number of ways = 7 . 5 . 3 . ^{8}C4 = 7 . ^{6}C4 . ^{8}C4.
How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?
120
480
360
240
C.
360
A total number of ways in which all letters can be arranged in alphabetical order = 6! There are two vowels in the word GARDEN. A total number of ways in which these two vowels can be arranged = 2!
∴ Total number of required ways
∴ Total number of required ways
If m is the AMN of two distinct real numbers l and n (l,n>1) and G_{1}, G_{2}, and G3 are three geometric means between l and n, then equals
4l^{2} mn
4lm^{2}n
4 lmn^{2}
4l^{2}m^{2}n^{2}
B.
4lm^{2}n
Given,
m is the AM of l and n
l +n = 2m
and G_{1}, G_{2}, G_{3}, n are in GP
Let r be the common ratio of this GP
G1 = lr
G2 =lr^{2}
G3= lr^{3}
n = lr^{4}
The number of integers greater than 6000 that can be formed, using the digits 3,5,6,7 and 8 without repetition, is
216
192
120
72
B.
192
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is
5
3^{8}
21
D.
21
The required number of ways